The knowledge of the electrical machine magnetic model is decisive in several aspects of its control, especially when strong nonlinearities of the flux linkage appear as in the synchronous reluctance machine. Examples of optimal tuning of PI-controllers in standard vector control are abundant in literature. Adapting the gain according to the machine model ensures the desired dynamics, and even becomes essential to prevent instability of the overall system. On top of that, the success of the most advanced control techniques, for example the Model Predictive Control, is subject to precise parameter knowledge.
Model knowledge also benefits the control by providing the knowledge of the decoupling terms arising from the Park transformation in the rotating dq reference frame. This is especially important when cross-magnetization effects occur. Only the proper compensation of these terms ensures optimal dynamics. Moreover, parameter knowledge implies that the motor can run at optimal performance and best efficiency, for instance according to the Maximum Torque per Ampere (MTPA) trajectory.
In the case of sensorless control, fundamental model-based methods require accurate parameter knowledge. By contrast, saliency-based sensorless control methods can determine the saliency position (geometric or saturation-induced saliency) without any knowledge of the machine parameters as long as cross-magnetisation effects can be neglected. However, when cross-magnetisation plays a role, a phase delay can introduce significant errors on the estimated angle, and therefore it must be estimated.
Last but not least, anomalous machine operation such as faults can be diagnosed on the basis of parameter intelligence. For this, the machine response is compared against an ideal model to detect deviations from the expected behaviour.
Machine parameter estimation can be grouped into two categories: offline and online methods. Offline methods are performed before operating the machine, while the online methods run during normal operation. The proposed solution is part of a class of offline methods known as self-commissioning methods, denoting that the identification of the machine model is performed without the requirement for additional equipment and solely by using the converter connected to the machine, of which the nameplate data are available.
Ideally, self-commissioning estimation methods are performed at standstill or quasi-standstill rotor condition, rendering manual locking and securing of the rotor redundant. Apart from being quicker, the advantages of standstill methods are first of all the maximum safety during the self-identification, as no running parts can harm personnel in the vicinity. Moreover, in contrast to constant-speed methods, no load machine is required. The need for a load machine is especially cumbersome if the machine has already been deployed at the customer facilities. Thirdly, the machine will be identified under the same conditions as during regular operation. This has the potential to include and compensate possible parasitic effects. The fourth and probably most beneficial advantage is the ability to identify the machine parameters on site without having to disconnect the load. This is especially useful for retrofitting purposes, for example when only the power converter is replaced. The other side of the coin, however, is that standstill tests cannot account for space harmonics, for example slot harmonics. In addition, the equipment of the drive system, for example the precision of the current sensors or the inverter nonlinearities, limits the accuracy.
The fact that a standstill estimation procedure runs before the normal operation of the drive gives great possibilities when it comes to injection of signals, as the negative side effects of injection such as torque ripple, noise, harmonics and switching losses are of lower concern during the limited time execution of the procedure. This time leaves also many degrees of freedom when choosing the switching frequency of the converter drive system.
Amongst the numerous procedures for standstill parameter estimation, many assume linear parameters and no cross-magnetization. Traditional procedures are described by IEEE standards, but they lack accuracy and are ineligible for a synchronous reluctance machine or an interior permanent magnet machine, as their strong nonlinearity dictates an operating point-dependent identification.
In some traditional procedures, as e.g. disclosed in B. Stumberger, G. Stumberger, D. Dolinar, A. Hamler, and M. Trlep, “Evaluation of saturation and cross-magnetization effects in interior permanent-magnet synchronous motor,” IEEE Transactions on Industry Applications, vol. 39, pp. 1264-1271, September-October 2003, the current of the orthogonal axis is held constant at different levels. To address the issue of thermal variation, the resistance is measured at each voltage step when the current levels off to a steady state. The flux is then recorded via the time integration of the back-electromotive force. The recorded flux tables are approximated by discrete partial derivatives to obtain the differential inductances. The problems with this approach are mostly related to the time integration, due to offsets in the voltage or current measurements, as this can result in the integrated value to drift away. In addition, the voltage level applied by the inverter is low and thus imprecise, especially when dealing with machines with small resistance values.
In a similar method, as disclosed in EP2453248 A1, a voltage pulse in direct or quadrature direction is applied. The flux is obtained according to a Tustin approximation of the time integral of the back-electromotive force, while considering the resistive voltage drop through sampling the current at a substantially high rate. This technique shares the same fundamental flaw of relying on time integration. Moreover, it does not give insight into how the resistance is obtained and lacks compensation of possible resistance variations stemming from thermal variations of the stator windings. Lastly, the work does not mention how the rotor is kept at standstill.
An improved method was proposed in WO 2013/017386. Also here, the current is following the rectangular reference waveform but instead of obtaining the flux by integration, a sinusoidal excitation signal is superimposed on the voltage reference as soon as the current has reached its steady state. The current response is measured and the differential inductance calculated. This is repeated for different amplitudes of the square waveform and the constant orthogonal current in order to cover all operating points. As the differential inductances are recorded, the overall flux can be procured by offline integration over current and a potential bias in the inductance measurement may at worst lead to a slightly less accurate flux linkage, but no drift-away is to be anticipated. On the other hand, the period of the sinusoid must consist of a certain number of PWM periods, forcing the current to stay in the same operating point for a length of time. This in turn may lead to a high speed build-up. On top of this, as different amplitudes of the square waveform are needed, the total duration of the estimation procedure is longer than methods that apply the maximum amplitude and determine the flux linkage while the current is changing.
Finally, all aforementioned methods share the flaw that while the mean torque is kept at zero, the mean speed has a discernible positive offset, causing the mechanical angle to drift away.
YI Li et al. “Improved Rotor-Position Estimation by Signal Injection in Brushless AC Motors Accounting for Cross-Coupling Magnetic Saturation”, IEEE Transactions on Industry Applications, IEEE Service Center, Piscataway, N.J., US, vol. 45, no. 5, 1 Sep. 2009 (2009 Sep. 1), pp. 1843-1850 discloses that the d- and q-axis incremental self-inductances, the incremental mutual inductance between the d-axis and the q-axis, and the cross-coupling factor are determined by finite-element analysis.